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tps: A theorem proving system for classical type theory
 Journal of Automated Reasoning
, 1996
"... This is a description of TPS, a theorem proving system for classical type theory (Church’s typed λcalculus). TPS has been designed to be a general research tool for manipulating wffs of first and higherorder logic, and searching for proofs of such wffs interactively or automatically, or in a comb ..."
Abstract

Cited by 71 (6 self)
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This is a description of TPS, a theorem proving system for classical type theory (Church’s typed λcalculus). TPS has been designed to be a general research tool for manipulating wffs of first and higherorder logic, and searching for proofs of such wffs interactively or automatically, or in a combination of these modes. An important feature of TPS is the ability to translate between expansion proofs and natural deduction proofs. Examples of theorems which TPS can prove completely automatically are given to illustrate certain aspects of TPS’s behavior and problems of theorem proving in higherorder logic. 7
Informationtheoretic Limitations of Formal Systems
 JOURNAL OF THE ACM
, 1974
"... An attempt is made to apply informationtheoretic computational complexity to metamathematics. The paper studies the number of bits of instructions that must be a given to a computer for it to perform finite and infinite tasks, and also the amount of time that it takes the computer to perform these ..."
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Cited by 45 (7 self)
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An attempt is made to apply informationtheoretic computational complexity to metamathematics. The paper studies the number of bits of instructions that must be a given to a computer for it to perform finite and infinite tasks, and also the amount of time that it takes the computer to perform these tasks. This is applied to measuring the difficulty of proving a given set of theorems, in terms of the number of bits of axioms that are assumed, and the size of the proofs needed to deduce the theorems from the axioms.
Type Checking with Universes
, 1991
"... Various formulations of constructive type theories have been proposed to serve as the basis for machineassisted proof and as a theoretical basis for studying programming languages. Many of these calculi include a cumulative hierarchy of "universes," each a type of types closed under a collectio ..."
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Cited by 24 (6 self)
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Various formulations of constructive type theories have been proposed to serve as the basis for machineassisted proof and as a theoretical basis for studying programming languages. Many of these calculi include a cumulative hierarchy of "universes," each a type of types closed under a collection of typeforming operations. Universes are of interest for a variety of reasons, some philosophical (predicative vs. impredicative type theories), some theoretical (limitations on the closure properties of type theories), and some practical (to achieve some of the advantages of a type of all types without sacrificing consistency.) The Generalized Calculus of Constructions (CC ! ) is a formal theory of types that includes such a hierarchy of universes. Although essential to the formalization of constructive mathematics, universes are tedious to use in practice, for one is required to make specific choices of universe levels and to ensure that all choices are consistent. In this pa...
Higher Order Logic
 In Handbook of Logic in Artificial Intelligence and Logic Programming
, 1994
"... Contents 1 Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 2 The expressive power of second order Logic : : : : : : : : : : : 3 2.1 The language of second order logic : : : : : : : : : : : : : 3 2.2 Expressing size : : : : : : : : : : : : : : : : : : : : : : : : 4 2.3 Definin ..."
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Cited by 19 (0 self)
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Contents 1 Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 2 The expressive power of second order Logic : : : : : : : : : : : 3 2.1 The language of second order logic : : : : : : : : : : : : : 3 2.2 Expressing size : : : : : : : : : : : : : : : : : : : : : : : : 4 2.3 Defining data types : : : : : : : : : : : : : : : : : : : : : 6 2.4 Describing processes : : : : : : : : : : : : : : : : : : : : : 8 2.5 Expressing convergence using second order validity : : : : : : : : : : : : : : : : : : : : : : : : : 9 2.6 Truth definitions: the analytical hierarchy : : : : : : : : 10 2.7 Inductive definitions : : : : : : : : : : : : : : : : : : : : : 13 3 Canonical semantics of higher order logic : : : : : : : : : : : : 15 3.1 Tarskian semantics of second order logic : : : : : : : : : 15 3.2 Function and re
Distinguishing Typing and Classification in Object Data Models
 In Information Modelling and Knowledge Bases, volume VI, chapter 25. IOS
, 1995
"... The notion of type has played a double role in database systems in that it has been used both to describe values stored in the database and also concepts of the application domain. In the context of object data models, we argue for a clear separation of these two roles into typing and classificatio ..."
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Cited by 17 (16 self)
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The notion of type has played a double role in database systems in that it has been used both to describe values stored in the database and also concepts of the application domain. In the context of object data models, we argue for a clear separation of these two roles into typing and classification, respectively. Typing is concerned with database representation while classification is concerned with models of reality in terms of entity categories and their interdependencies. We discuss this distinction and the benefits that it affords in terms of both conceptual modelling and object data model genericity. 1 Introduction There has been much discussion on the role of "type" in the fields of Programming Languages, Data Models and Knowledge Representation (see for example [BMe84, BZ81]). The debate centres on such issues as whether "type" is an intensional or extensional notion. In the case where it is intensional, there are further differences as to whether it is definitional in that i...
A firstorder theory of communication and multiagent plans
 Journal of Logic and Computation
"... This paper presents a theory expressed in firstorder logic for describing and supporting inference about action, knowledge, planning, and communication, in an egalitarian multiagent setting. The underlying ontology of the theory uses a situationbased temporal model and a possibleworlds model of ..."
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Cited by 17 (6 self)
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This paper presents a theory expressed in firstorder logic for describing and supporting inference about action, knowledge, planning, and communication, in an egalitarian multiagent setting. The underlying ontology of the theory uses a situationbased temporal model and a possibleworlds model of knowledge. It supports plans and communications of a very general kind, both informative communications and requests. Communications may refer to states of the world or states of knowledge in the past, present, or future. We demonstrate that the theory is powerful enough to represent several interesting multiagent planning problems and to justify their solutions. We have proven that the theory of knowledge, communication, and planning is consistent with a broad range of physical theories, despite the existence of a number of potential paradoxes.
TPS: A TheoremProving System for Classical Type Theory
, 1996
"... . This is description of TPS, a theoremproving system for classical type theory (Church's typed #calculus). TPS has been designed to be a general research tool for manipulating wffs of first and higherorder logic, and searching for proofs of such wffs interactively or automatically, or in a comb ..."
Abstract

Cited by 16 (0 self)
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. This is description of TPS, a theoremproving system for classical type theory (Church's typed #calculus). TPS has been designed to be a general research tool for manipulating wffs of first and higherorder logic, and searching for proofs of such wffs interactively or automatically, or in a combination of these modes. An important feature of TPS is the ability to translate between expansion proofs and natural deduction proofs. Examples of theorems that TPS can prove completely automatically are given to illustrate certain aspects of TPS's behavior and problems of theorem proving in higherorder logic. AMS Subject Classification: 0304, 68T15, 03B35, 03B15, 03B10. Key words: higherorder logic, type theory, mating, connection, expansion proof, natural deduction. 1. Introduction TPS is a theoremproving system for classical type theory ## (Church's typed #calculus [20]) which has been under development at Carnegie Mellon University for a number years. This paper gives a general...
An ontology of data modelling languages: a study using a commonsense realistic ontology
 Journal of Database Management
, 2004
"... Data modelling languages are used in today’s information systems engineering environments. Many have a degree of hype surrounding their quality and applicability with narrow and specific justification often given in support of one over another. We want to more deeply understand the fundamental natur ..."
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Cited by 15 (2 self)
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Data modelling languages are used in today’s information systems engineering environments. Many have a degree of hype surrounding their quality and applicability with narrow and specific justification often given in support of one over another. We want to more deeply understand the fundamental nature of data modelling languages. We thus propose a theory, based on ontology, that should allow us to understand, compare, evaluate, and strengthen data modelling languages. In this paper we present a method (conceptual evaluation) and its extension (conceptual comparison), as part of our theory. Our methods are largely independent of a specific ontology. We introduce Chisholm’s ontology and apply our methods to analyse some data modelling languages using it. We find a good degree of overlap between all of the data modelling languages analysed and the core concepts of Chisholm’s ontology, and conclude that the data modelling languages investigated reflect an ontology of commonsenserealism.